Exact inequalities and optimal recovery by inaccurate information
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908316599320576 |
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| author | Osipenko, K. Yu. |
| author_facet | Osipenko, K. Yu. |
| contents | The paper considers a multidimensional problem of optimal recovery of an operator whose action is represented by multiplying the original function by a weight function of a special type, based on inaccurately specified information about the values of operators of a similar type. An exact inequality for the norms of such operators is obtained. The problem under consideration is a generalization of the problem of optimal recovery of a derivative based on other inaccurately specified derivatives in the space $\mathbb R^d$ and the problem of an exact inequality, which is an analogue of the Hardy-Littlewood-Polya inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09139 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact inequalities and optimal recovery by inaccurate information Osipenko, K. Yu. Numerical Analysis 26DD15, 41A65, 41A46, 49N30 The paper considers a multidimensional problem of optimal recovery of an operator whose action is represented by multiplying the original function by a weight function of a special type, based on inaccurately specified information about the values of operators of a similar type. An exact inequality for the norms of such operators is obtained. The problem under consideration is a generalization of the problem of optimal recovery of a derivative based on other inaccurately specified derivatives in the space $\mathbb R^d$ and the problem of an exact inequality, which is an analogue of the Hardy-Littlewood-Polya inequality. |
| title | Exact inequalities and optimal recovery by inaccurate information |
| topic | Numerical Analysis 26DD15, 41A65, 41A46, 49N30 |
| url | https://arxiv.org/abs/2504.09139 |